Transcription of Preface - Cornell University
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Preface - Cornell University
Preface .. ix Standard Notations xii. Chapter 0. Some Underlying Geometric Notions .. 1. Homotopy and Homotopy Type 1. Cell Complexes 5. Operations on Spaces 8. Two Criteria for Homotopy Equivalence 10. The Homotopy Extension Property 14. Chapter 1. The Fundamental Group .. 21. Basic Constructions .. 25. Paths and Homotopy 25. The Fundamental Group of the Circle 29. Induced Homomorphisms 34. Van Kampen's Theorem .. 40. Free Products of Groups 41. The van Kampen Theorem 43. Applications to Cell Complexes 49. Covering Spaces .. 56. Lifting Properties 60. The Classification of Covering Spaces 63. Deck Transformations and Group Actions 70. Additional Topics Graphs and Free Groups 83. K(G,1) Spaces and Graphs of Groups 87. Chapter 2.
Dn: the unit disk or ball in Rn, all points of distance ≤1 from the origin. ∂Dn=Sn−1: the boundary of the ndisk. en: an ncell, homeomorphic to the open ndisk Dn−∂Dn. In particular, D0 and e0 consist of a single point since R0 ={0}. But S0 consists of two points since it is ∂D1. 11 : the identity function from a set to itself. `
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